Metamagic is widely considered to be one of the most tried and tested methods of breaking the game. Certainly, I have little doubt that the "something for nothing" deals that approaches that allow you to get metamagic for free (or as good as) are unbalanced (e.g. that Divine Metamagic feat). However, the general opinion seems to be that metamagic in of itself is enough to upset the balance. Why is this?
Note 1: Any answer that goes for the "metamagic is fine, but how cheap you can get it is what breaks it" angle ought to be explain why/how it's so easy to get cheaply. We all know about the Incantrix, but it's worth showing the numbers.
Note 2: Some metamagic feats obviously suck. If the issue is not with the metamagic mechanic in of itself, but actually that some metamagic feats are simply overpowered, then name and explain them.
Best Answer
Certainly, some metamagic effects will never break the game. No one cares about Enlarge Spell or Widen Spell in most cases, and Heighten Spell is problematic only in niche cases.¹ Energy Substitution enables shenanigans with Snowcasting, but ultimately the only truly problematic case is the locate city bomb, which is of dubious legality and exceptionally specific anyway. Dragon magazine has a bunch of metamagic feats that I’d be hard-pressed to break.²
On the other hand, some metamagic effects are just clearly strong—anything that lets you have more spells at a time, for instance.³ However, all of these were expected to be fairly strong, and their costs were set accordingly. Quicken Spell is exceedingly strong, but casting a spell that’s eight levels old is rough. These are the typical targets of metamagic reducing, e.g. incantatrix, Arcane Thesis, even just Easy and/or Practical Metamagic. Especially if you can get things to the point that you can use these metamagic effects on every spell you cast, that is incredibly potent. Stuff that provides alternative ways to pay (e.g. Divine Metamagic, Metamagic Song, etc.) is less overpowered with most of these, since as a few/day ability they are strong but not broken—but Persist Spell is the obvious exception there, since you only need it a few times per day.
Even without doing that, though, some spells—enervation, most famously—are just incredibly amenable to metamagic. Even if you need a pair of 9th-level spell slots to do it, a ray-splitting ray-extension empowered enervation followed by a quickened ray-extension enervation can dole out an average of 27½ negative levels in two rounds, which is astoundingly dangerous.
A mailman build, of course, does great things with orb of fire and Searing Spell, or orb of cold and Piercing Cold, and a bunch of other metamagic. Metamagic discounts are the best way to do it, of course, but the general concept remains sound without them, at least at higher levels.
But these are all just strong. They are certainly overpowered relative to CR, or relative to the capabilities of most characters, but they aren’t necessarily game-breaking. People can, and do, play games where people are leveraging these things, even with incantatrix et al.
Game-breaking mostly comes from effects that aren’t especially strong, but in corner cases, well, breaks the rules. Sanctum Spell is garbage for what it actually does, but has so many ways of breaking the rules around spell levels, in both directions even. Consider that Sanctum Spell’s reduction of spell level allows it to be included in a spell matrix or an eldritch tapestry when it otherwise couldn’t. And of course, in your sanctum, the free Heighten effect can mean early entry. That is game-breaking, in that you simply aren’t supposed to be able to do those things, rather than just being overpowered, because you’re able to get more than you should be able to afford. But people play those sorts of games, too.
Ultimately, I’d say the real biggest problem with metamagic in 3.5e is that without discounts, it’s kind of overpriced. You’d get Quicken at the highest levels, and Extend is cheap enough to be worthwhile, but otherwise it’s very dubious to really use much metamagic without discounts or alternative payments. Once you introduce those things, of course, it quickly gets out of hand. That’s a headache.
But none of that means that there can’t be a balance, or that the concept is inherently imbalanced. It just means that 3.5e doesn’t quite hit the sweet spot most of the time for most tables.
I.e. when you use Heighten Spell with metamagic-discount effects to count as casting higher-level spells than you actually can in order to access feats or prestige classes earlier than you’re supposed to.
Looking through a list, I don’t see any way to break the game with any of Bend Spell, Clawed Spell, Named Spell, Piercing Spell, Ray Burst, Ray Coning, and Relicguard Spell.
E.g. Ocular Spell, Quicken Spell, Ray Splitting, Repeat Spell. I’ll put Persist Spell in this group, too, because it allows you to have pre-cast buff spells that you otherwise would have had to cast mid-combat.